Acronym ...
Name 2srid (?)
Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figure 2[3,4,10/2,4] (type A) or
2[6/2,4,5,4] (type B) or
2[6/2,4,10/2,4] (type C)
Snub derivation
 (type A)    (type B)    (type C)
General of army srid
Colonel of regiment srid
Confer
non-Grünbaumian master:
srid  

Looks like a compound of 2 small rhombicosidodecahedra (srid), and indeed vertices, edges, and {4} coincide by pairs (type C). For type A additionally {3} resp. for type B additionally {5} coincide by pairs as well.


Incidence matrix according to Dynkin symbol

β3β5x   (type A)

demi( . . . (a)) | 60  * |  1  2  0  1 |  1  0  1  2
demi( . . . (b)) |  * 60 |  1  0  2  1 |  0  1  1  2
-----------------+-------+-------------+------------
both( . . x    ) |  1  1 | 60  *  *  * |  0  0  1  1
sefa( s3s . (a)) |  2  0 |  * 60  *  * |  1  0  0  1
sefa( s3s . (b)) |  0  2 |  *  * 60  * |  0  1  0  1
sefa( . β5x    ) |  1  1 |  *  *  * 60 |  0  0  1  1
-----------------+-------+-------------+------------
      s3s . (a)    3  0 |  0  3  0  0 | 20  *  *  *
      s3s . (b)    0  3 |  0  0  3  0 |  * 20  *  *
      . β5x        5  5 |  5  0  0  5 |  *  * 12  *
sefa( β3β5x    ) |  2  2 |  1  1  1  1 |  *  *  * 60
or
both( . . . ) | 120 |  1   2  1 |  1  1  2
--------------+-----+-----------+---------
both( . . x ) |   2 | 60   *  * |  0  1  1
sefa( s3s . ) |   2 |  * 120  * |  1  0  1
sefa( . β5x ) |   2 |  *   * 60 |  0  1  1
--------------+-----+-----------+---------
both( s3s . )    3 |  0   3  0 | 40  *  *
      . β5x     10 |  5   0  5 |  * 12  *
sefa( β3β5x ) |   4 |  1   2  1 |  *  * 60

starting figure: x3x5x

β5β3x   (type B)

demi( . . . (a)) | 60  * |  1  2  0  1 |  1  0  1  2
demi( . . . (b)) |  * 60 |  1  0  2  1 |  0  1  1  2
-----------------+-------+-------------+------------
both( . . x    ) |  1  1 | 60  *  *  * |  0  0  1  1
sefa( s5s . (a)) |  2  0 |  * 60  *  * |  1  0  0  1
sefa( s5s . (b)) |  0  2 |  *  * 60  * |  0  1  0  1
sefa( . β3x    ) |  1  1 |  *  *  * 60 |  0  0  1  1
-----------------+-------+-------------+------------
      s5s . (a)    5  0 |  0  5  0  0 | 12  *  *  *
      s5s . (b)    0  5 |  0  0  5  0 |  * 12  *  *
      . β3x        3  3 |  3  0  0  3 |  *  * 20  *
sefa( β5β3x    ) |  2  2 |  1  1  1  1 |  *  *  * 60
or
both( . . . ) | 120 |  1   2  1 |  1  1  2
--------------+-----+-----------+---------
both( . . x ) |   2 | 60   *  * |  0  1  1
sefa( s5s . ) |   2 |  * 120  * |  1  0  1
sefa( . β3x ) |   2 |  *   * 60 |  0  1  1
--------------+-----+-----------+---------
both( s5s . )    5 |  0   5  0 | 24  *  *
      . β3x      6 |  3   0  3 |  * 20  *
sefa( β5β3x ) |   4 |  1   2  1 |  *  * 60

starting figure: x5x3x

x3β5x   (type C)

both( . . . ) | 120 |  1  1  1  1 |  1  1  1  1
--------------+-----+-------------+------------
both( x . . ) |   2 | 60  *  *  * |  1  0  1  0
both( . . x ) |   2 |  * 60  *  * |  0  1  1  0
sefa( x3β . ) |   2 |  *  * 60  * |  1  0  0  1
sefa( . β5x ) |   2 |  *  *  * 60 |  0  1  0  1
--------------+-----+-------------+------------
      x3β .      6 |  3  0  3  0 | 20  *  *  *
      . β5x     10 |  0  5  0  5 |  * 12  *  *
both( x . x ) |   4 |  2  2  0  0 |  *  * 30  *
sefa( x3β5x ) |   4 |  0  0  2  2 |  *  *  * 30

starting figure: x3x5x

© 2004-2019
top of page